MinT - Information on Result #1115526

Information on Result #1115526

Linear OOA(2¹⁴⁶, 4194306, F₂, 5, 11) (dual of [(4194306, 5), 20971384, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶, 5, F₂, 5, 5) (dual of [(5, 5), 19, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁶, 5, F₂, 4, 5) (dual of [(5, 4), 14, 6]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,14P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
    - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁴⁰, 4194301, F₂, 5, 11) (dual of [(4194301, 5), 20971365, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2¹⁴⁰, 8388602, F₂, 3, 11) (dual of [(8388602, 3), 25165666, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2¹⁴⁰, large, F₂, 3, 11), using
    - OOAs constructed from BCH codes [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁴⁶, 4194305, F₂, 6, 11) (dual of [(4194305, 6), 25165684, 12]-NRT-code)	[i]	OOA Stacking with Additional Row
2	Linear OOA(2¹⁴⁶, 4194305, F₂, 7, 11) (dual of [(4194305, 7), 29359989, 12]-NRT-code)	[i]
3	Linear OOA(2¹⁴⁶, 4194305, F₂, 8, 11) (dual of [(4194305, 8), 33554294, 12]-NRT-code)	[i]
4	Linear OOA(2¹⁴⁶, 4194305, F₂, 15, 11) (dual of [(4194305, 15), 62914429, 12]-NRT-code)	[i]